Dimensionally regularized Tsallis' Statistical Mechanics and two-body Newton's gravitation

TL;DR

This paper applies dimensional regularization to address poles in Tsallis' statistical mechanics, analyzing their effects on specific heats in a two-body gravitational system, thus advancing the understanding of non-extensive thermodynamics.

Contribution

It introduces a dimensional regularization approach to handle poles in Tsallis' statistical mechanics and studies their impact on gravitational systems.

Findings

Poles occur at specific rational values of q in Tsallis' statistics.

Dimensional regularization effectively manages these poles.

Poles influence the specific heat behavior in gravitational systems.

Abstract

Typical Tsallis' statistical mechanics' quantifiers like the partition function and the mean energy exhibit poles. We are speaking of the partition function ${\cal Z}$ and the mean energy $<{\cal U}>$. The poles appear for distinctive values of Tsallis' characteristic real parameter $q$, at a numerable set of rational numbers of the $q-$line. These poles are dealt with dimensional regularization resources. The physical effects of these poles on the specific heats are studied here for the two-body classical gravitation potential.